Journal of Nonlinear Mathematical Physics

Volume 10, Issue Supplement 2, December 2003, Pages 166 - 180

The Hasse-Weil Bound and Integrability Detection in Rational Maps

Authors
John A.G. Roberts, Danesh Jogia, Franco Vivaldi
Corresponding Author
John A.G. Roberts
Available Online 1 December 2003.
DOI
10.2991/jnmp.2003.10.s2.15How to use a DOI?
Abstract

We reduce planar measure-preserving rational maps over finite fields, and study their discrete dynamics. We show that application to the orbit analysis over these fields of the Hasse-Weil bound for the number of points on an algebraic curve gives a strong indication of the existence of an integral for the map. Moreover, the method is ideally suited to separating near-integrability from genuine integrability.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - Supplement 2
Pages
166 - 180
Publication Date
2003/12/01
ISBN
91-974824-0-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2003.10.s2.15How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - John A.G. Roberts
AU  - Danesh Jogia
AU  - Franco Vivaldi
PY  - 2003
DA  - 2003/12/01
TI  - The Hasse-Weil Bound and Integrability Detection in Rational Maps
JO  - Journal of Nonlinear Mathematical Physics
SP  - 166
EP  - 180
VL  - 10
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.s2.15
DO  - 10.2991/jnmp.2003.10.s2.15
ID  - Roberts2003
ER  -